NOMISMA
History's lessons for today's decisions / Calculate with Your Own Numbers

Calculating the decrease from fees and inflation

How much an annual percentage fee and an annual percentage inflation will reduce one's savings over a number of years.

Fees and Inflation's Impact in 3 Minutes

  1. See it
  2. In numbers
  3. What would you do?
  4. Read more

1See it

Swipe to see more

1 / 8

Fees are deducted from your balance every year.

2 / 8

If the fee is 1 percent a year, you multiply your balance by 0.99 every year.

3 / 8

Investing $100,000 at 4 percent a year for 20 years.

With a 0.25 percent annual fee, you'd have about $208,000.

4 / 8

With a 1.00 percent annual fee, you'd have about $179,000.

5 / 8

2025 average

Consumer prices rose 3.2 percent from the previous year.

6 / 8

Inflation reduces how much you can buy with the same amount of money.

7 / 8

Fees and inflation have separate effects. Let's look at them together.

8 / 8

This calculation does not include investment returns.

2In numbers

179000dollars

About $179,000. From $100,000 invested at 4 percent for 20 years with a 1.00 percent annual fee.

Annual fee: 0.25%About $208,000
Annual fee: 1.00%About $179,000

3What would you do?

Your statement shows a '1% annual' fee, and the news says prices are rising. What is affecting your savings?

Pick one

Just the fees

Fees reduce your balance. Inflation reduces how much you can buy with the same amount of money. Since they have separate effects, we look at them together.

Just inflation

Inflation reduces how much you can buy. Fees separately reduce your balance. Looking at both together shows you the forces at work on your savings.

Both

That's right. If you enter the fee, inflation rate, and number of years into the calculator, it will show you the value after accounting for both.

4Read more

Read the full story ↓

When to use When you see the fee rate on a statement. When you want to apply news about the inflation rate to your own savings.

Cumulative fees

Fees are deducted from the balance each year. If the annual fee is one percent, you multiply the balance by zero point nine nine for the number of years. In an example from the U.S. Securities and Exchange Commission, an investment of one hundred thousand dollars earning four percent annually for twenty years would be worth approximately two hundred and eight thousand dollars with a zero point two five percent annual fee, and approximately one hundred and seventy-nine thousand dollars with a one point zero zero percent annual fee.

Reduction due to inflation

Dividing the nominal amount by one plus the inflation rate raised to the power of the number of years gives the real value. The average consumer price index for 2025 showed an overall increase of three point two percent from the previous year. In the U.S., it was three point four percent for the twelve months ending July 2026.

The two have separate effects

Fees reduce the balance, and inflation reduces purchasing power. Viewing both in the same table reveals the forces at work on your savings. This calculation does not include investment returns. Prospective returns are not covered in this subject.

Try with your own numbers

If you change the numbers, it recalculates on the spot. The formula is written below.

Input value

Output value

Cumulative amount reduced by fees(Yen)—
Balance after deducting fees(Yen)—
Real value adjusted for inflation (no fees)(Yen)—
Value after deducting fees and adjusting for inflation(Yen)—

Formula Cumulative amount reduced by fees = Principal × (1 - (1 - Fee ÷ 100) ^ Number of years). Real value = Principal ÷ (1 + Inflation Rate ÷ 100) ^ Number of years

In other countries

The U.S. Securities and Exchange Commission advises that even with deposits, there is a risk that interest rates will not keep up with inflation. The consumer price index is published monthly by the Statistics Bureau of Japan and by the Bureau of Labor Statistics in the U.S. The formula is the same; the rates used differ by country and time.

Bibliography

Related Lectures and Notes

P6 P2 P5

Back to "Everyday Money: Calculations and Procedures" list

Price

After purchase, the full courses, the illustrated books, every country’s story and the numismatics examination are open to you.

See the price →